Geometric and nonequilibrium criticality in run-and-tumble particles with competing motility and attraction

Self-propulsion in run-and-tumble particles (RTPs) generates effective attractive interactions that can drive motility-induced phase separation (MIPS), a phenomenon absent in passive systems. Here we investigate RTPs in the presence of explicit attractive interactions and show that, at high motility, such interactions can suppress MIPS, yielding a homogeneous phase. Upon further increasing the attraction strength, phase separation reappears, giving rise to a re-entrant transition. We characterize this transition by analyzing the percolation properties of dense clusters, which provide geometric signatures of phase separation. Along the resulting critical line, we find continuously varying critical exponents, while certain scaling functions remain unchanged and coincide with those of equilibrium lattice gas models undergoing interacting percolation, which is in the Ising-percolation universality class. These results reveal that the MIPS transition in interacting RTP systems exhibit Ising superuniversality, thereby establishing a connection between nonequilibrium active matter and classical critical behavior.